$\"\"$

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The linear equation is $\"\"$ ; $\"\"$ .

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Find slope.

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$\"\"$ (Slope-intercept form)

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$\"\"$ (Original equation)

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Compare the equation with slope-intercept form and find the slope of the line.

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Slope of the line $\"\"$ .

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$\"\"$

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Find the perpendicular line equation.

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The slope of the perpendicular line is negative reciprocal $\"\"$ .

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$\"\"$ (Point-slope form)

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$\"\"$ (Substitute $\"\"$ and $\"\"$ )

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$\"\"$ (Simplify)

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$\"\"$ (Cross product)

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$\"\"$ (Distributive property: $\"\"$ )

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$\"\"$ (Subtract $\"\"$ from each side)

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$\"\"$ (Apply additive inverse property: $\"\"$ )

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Cancel common terms).

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Therefore, the slope-intercept form perpendicular line equation is $\"\"$ .

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$\"\"$

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The slope-intercept form in perpendicular line equation is $\"\"$ .